Nodal $d+id$ pairing and topological phases on the triangular lattice: unconventional superconducting state of Na$_x$CoO$_2\cdot y$H$_2$O

TL;DR

This paper investigates the topological properties of chiral $d+id$-wave superconductivity on a triangular lattice, revealing a doping-induced quantum phase transition with potential relevance to the unconventional superconductor Na$_x$CoO$_2\, y$H$_2$O.

Contribution

It demonstrates that $d+id$ pairing on the triangular lattice exhibits topological phase transitions at specific doping levels, linking the pairing symmetry to the material's unconventional superconductivity.

Findings

Identification of a topological quantum phase transition at critical doping $x_c \,\approx 0.25$.

Presence of six Dirac points at the critical state.

Explanation of the unconventional superconducting state of Na$_x$CoO$_2\cdot y$H$_2$O.

Abstract

We show that finite angular momentum pairing chiral superconductors on the triangular lattice have point zeroes in the complex gap function. A topological quantum phase transition takes place through a nodal superconducting state at a specific carrier density $x_c$ where the normal state Fermi surface crosses the isolated zeros. For spin singlet pairing, we show that the second nearest neighbor $d+id$-wave pairing can be the dominant pairing channel. The gapless critical state at $x_c\simeq0.25$ has six Dirac points and is topologically nontrivial with a $T^3$ spin relaxation rate below $T_c$. This picture provides a possible explanation for the unconventional superconducting state of Na$_x$CoO$_2\cdot y$H$_2$O. Analyzing a pairing model with strong correlation using the Gutzwiller projection and symmetry arguments, we study these topological phases and phase transitions as a function of Na doping.